scholarly journals On the anticrowding population dynamics taking into account a discrete set of offspring

2015 ◽  
Vol 56 ◽  
Author(s):  
Šarūnas Repšys ◽  
Vladas Skakauskas
Keyword(s):  
Population Dynamics ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Type A ◽  
Numerical Results ◽  
Integral Type ◽  
Partial Differential ◽  
Directed Diffusion

A model of a population dynamics is solved numerically taking into account a discrete set of offsprings and the nonlinear (directed) diffusion. The model consists of a system of integro-partial differential equations subject to conditions of integral type. A spread of initially lokalized population is studied. Some numerical results are discussed.

Extrapolating for attaining high precision solutions for fractional partial differential equations

2018 ◽  
Vol 21 (6) ◽  
pp. 1506-1523 ◽  
Author(s):  
Fernanda Simões Patrício ◽  
Miguel Patrício ◽  
Higinio Ramos
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
High Precision ◽  
Euler Method ◽  
Accurate Solution ◽  
Numerical Results ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Temporal Integrator ◽  
Present Technique

Abstract This paper aims at obtaining a high precision numerical approximation for fractional partial differential equations. This is achieved through appropriate discretizations: firstly we consider the application of shifted Legendre or Chebyshev polynomials to get a spatial discretization, followed by a temporal discretization where we use the Implicit Euler method (although any other temporal integrator could be used). Finally, the use of an extrapolation technique is considered for improving the numerical results. In this way a very accurate solution is obtained. An algorithm is presented, and numerical results are shown to demonstrate the validity of the present technique.

Partial Differential Equations in Ecology: Spatial Interactions and Population Dynamics

Ecology ◽  
1994 ◽  
Vol 75 (1) ◽  
pp. 17-29 ◽  
Author(s):  
E. E. Holmes ◽  
M. A. Lewis ◽  
J. E. Banks ◽  
R. R. Veit
Keyword(s):  
Population Dynamics ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Spatial Interactions ◽  
Partial Differential

scholarly journals Passivity-Based Control of Rotational and Translational Timoshenko Arms

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Minoru Sasaki ◽  
Takeshi Ueda ◽  
Yshihiro Inoue ◽  
Wayne J. Book
Keyword(s):  
Partial Differential Equations ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Tracking Control ◽  
Numerical Results ◽  
Timoshenko Model ◽  
Partial Differential ◽  
Control Schemes ◽  
Passivity Based Control ◽  
Conventional Methods

It is shown that the alternate passivity-based control schemes can be designed which explicitly exploit the passivity properties of the Timoshenko model. This approach has the advantage over the conventional methods in the respect that it allows one to deal directly with the system's partial differential equations without resorting to approximations. Numerical results for the tracking control of a translational and rotational flexible Timoshenko arm are presented and compared. They verify that the proposed control schemes are effective at controlling flexible dynamical systems.

B-spline wavelet operational method for numerical solution of time-space fractional partial differential equations

2017 ◽  
Vol 15 (04) ◽  
pp. 1750034 ◽  
Author(s):  
Zeynab Kargar ◽  
Habibollah Saeedi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Results ◽  
Scaling Functions ◽  
Operational Matrices ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
B Spline ◽  
Time Space ◽  
Linear B

In this paper, the linear B-spline scaling functions and wavelets operational matrix of fractional integration are derived. A new approach implementing the linear B-spline scaling functions and wavelets operational matrices combining with the spectral tau method is introduced for approximating the numerical solutions of time-space fractional partial differential equations with initial-boundary conditions. They are utilized to reduce the main problem to a system of algebraic equations. The uniform convergence analysis for the linear B-spline scaling functions and wavelets expansion and an efficient error estimation of the presented method are also introduced. Illustrative examples are given and numerical results are presented to demonstrate the efficiency and accuracy of the proposed method. Special attention is given to a comparison between the numerical results obtained by our new technique and those found by other known methods.

scholarly journals New Perspective on the Conventional Solutions of the Nonlinear Time-Fractional Partial Differential Equations

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
Hijaz Ahmad ◽  
Ali Akgül ◽  
Tufail A. Khan ◽  
Predrag S. Stanimirović ◽  
Yu-Ming Chu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Numerical Results ◽  
Iteration Algorithm ◽  
Partial Differential ◽  
Novel Approach ◽  
New Perspective

The role of integer and noninteger order partial differential equations (PDE) is essential in applied sciences and engineering. Exact solutions of these equations are sometimes difficult to find. Therefore, it takes time to develop some numerical techniques to find accurate numerical solutions of these types of differential equations. This work aims to present a novel approach termed as fractional iteration algorithm-I for finding the numerical solution of nonlinear noninteger order partial differential equations. The proposed approach is developed and tested on nonlinear fractional-order Fornberg–Whitham equation and employed without using any transformation, Adomian polynomials, small perturbation, discretization, or linearization. The fractional derivatives are taken in the Caputo sense. To assess the efficiency and precision of the suggested method, the tabulated numerical results are compared with the standard variational iteration method and the exact solution as well. In addition, numerical results for different cases of the fractional-order α are presented graphically, which show the effectiveness of the proposed procedure and revealed that the proposed scheme is very effective, suitable for fractional PDEs, and may be viewed as a generalization of the existing methods for solving integer and noninteger order differential equations.

The domain of analyticity of Dirichlet–Neumann operators

2010 ◽  
Vol 140 (2) ◽  
pp. 367-389 ◽  
Author(s):  
Bei Hu ◽  
David P. Nicholls
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Taylor Series ◽  
Series Representation ◽  
Elliptic Partial Differential Equations ◽  
Numerical Results ◽  
Partial Differential ◽  
Boundary Shape ◽  
Analytical Properties

Dirichlet–Neumann operators arise in many applications in the sciences, and this has inspired a number of studies on their analytical properties. In this paper we further investigate the analyticity properties of Dirichlet–Neumann operators as functions of the boundary shape. In particular, we study the size of the disc of convergence of their Taylor-series representation. For this we use a complexification technique which requires a novel reformulation of the problem, coupled with methods for systems of elliptic partial differential equations. Numerical results to illustrate our theoretical conclusions are presented.

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